Method of and apparatus for controlling moisture content of a web product at the time of changing the grade of the web product on a paper machine

ABSTRACT

A paper-making process control system is provided for a paper making machine to simulate a web drying operation performed by the drying sections of the paper machine, in order to enhance the reliability of controlling operation in the web product grade change and to reduce the time necessary for the grade change. In the control system, when a web product change is carried out during the paper-making process by passing a web (WE) along with a canvas belt (14b) around a steam-heated drums (14a) for the drying of the web (WE), the control system describes heat balance among the steam-heated drums(14a), the web (WE), and the canvas belt (14b) by heat balance equations on an assumption that there is no temperature differential in the temperature of the circumferential portion of each steam-heated drum (14a), and adjustably regulates supply of steam to the respective steam-heated drums (14a) on the basis of the heat balance equations to thereby bring a moisture content of the web (WE) to a desired value.

TECHNICAL FIELD

The present invention relates to a method of simulating a steady statemoisture content of a web product on a paper machine in which a web (amoist web) along with a canvas belt are passed around the steam-heateddrums of a drying section to dry the web, and an apparatus for carryingout the above-mentioned method. More specifically, the present inventionrelates to a method of simulating the effect of varying the pressure ofsteam supplied to steam-heated drums of a paper machine on the moisturecontent of a web product during an unsteady transferring state in thepaper producing process in which a moist web and a canvas belt are fedaround steam-heated drums in the paper machine to obtain the dried webproduct, and an apparatus for carrying out the method.

The present invention also relates to a method of controlling themoisture content of a web so that the moisture content of the web isadjusted to a desired moisture content when a grade of a web product ona paper machine, in which a moist web along with a canvas belt arepassed around steam-heated drums thereof to dry the web, should bechanged from one web product grade to a different web product grade, anda control apparatus for carrying out such method.

BACKGROUND ART

As is generally known, a typical paper machine has a wire section, apress section, a predrying section, a sizing section, and an afterdryingsection. The wire section includes an endless wire belt, and a stockinlet unit is disposed at the receiving end of the wire section. Paperstock, i.e., pulp, is discharged from the stock inlet unit into the wiresection. Water contained in the paper stock is drained in the wiresection to form a web. The web is delivered from the wire section to thepress section and the web is further drained of water in the presssection, and then the web is delivered, as a moist web, to the predryingsection. A plurality of steam-heated drums are arranged in the predryingsection and are heated by steam supplied thereto. The moist web is woundsequentially around the steam-heated drums of the predrying section andis dried by the steam-heated drums to a predetermined moisture content.Subsequently, the web is subjected to a sizing process in the sizingsection, and then the sized web is further dried to have a predeterminedmoisture content while the sized web passes through the afterdryingsection. The construction and arrangement of the afterdrying section aresubstantially the same as that of the predrying section. After beingthus dried in the afterdrying section, the web is taken up in a roll asa final product.

The basis weight and the moisture content of the web must be measured atthe outlet of the afterdrying section and the paper stock discharge rateat which the paper stock is discharged into the wire section and thesteam pressures in the steam-heated drums must be controlled on thebasis of measured data. Such control operations are carried out by abasis weight and moisture measuring system (hereinafter referred to as"BM measuring system"). The BM measuring system is provided withmeasuring units disposed just behind the predrying section and theafterdrying section, respectively, and a control unit for processingdata provided by the respective measuring units. In short, paper stockdischarge rate at which the paper stock is discharged into the wiresection, the pressure of the steam supplied to the steam-heated drumsand such are controlled on the basis Of the data provided by themeasuring units, i.e., the basis weight and the moisture content of theweb, the web speed of the paper machine, and such, to produce a webhaving uniform quality.

A paper-making process condition control function to control a change inthe grade of a web product from one to a different grade is one of thecontrol functions of the BM measuring system. Namely, according to thepaper-making process condition control function, the control unitchanges, while the paper machine is operating continuously, paper-makingprocess conditions, including paper stock discharge rate and thepressure of the steam, after the completion of a paper-making processfor producing a web of, for example, a given basis weight and anotherpaper-making process for producing a web of another basis weight isstarted. Although the steam pressure for the steam-heated drums, the webspeed and such are changed greatly when changing process conditions forone paper-making process to those for another, i.e, when changing thegrade of the web product from one to another, the steam pressure for thesteam-heated drums and such are predicted on the basis of accumulatedmeasured data by using a simple predictive equation and the paper-makingprocess conditions are controlled according to estimated values tochange the process conditions for the preceding paper-making process tothose for the succeeding paper-making process; that is, the steampressure for the steam-heated drums of the predrying section areregulated properly so that the moisture content of a web of a new basisweight immediately after drying by the predrying section is adjusted toa desired moisture content, and the steam pressure for the steam-heateddrums of the after-drying section are controlled properly so that themoisture content of the web immediately after drying by the afterdryingsection is adjusted to a desired moisture content.

Incidentally, the web produced during a transient paper-making operationbetween the preceding paper-making process to the succeedingpaper-making process, i.e., during a period in which the paper-makingprocess conditions are varied (the grade of web product is changed) is asubstandard web, i.e., a waste web. Therefore, the time necessary forchanging paper-making process conditions must be reduced to the leastpossible extent to improve the production efficiency of the papermachine. Nevertheless, paper-making process condition control by theconventional BM measuring system is unable to achieve satisfactorymoisture content control for all the cases of paper-making processcondition change. The unsatisfactory moisture content control isconsidered to be due to the paper-making process condition control basedon empirical predictive equations not theoretically substantiated andthe control of the paper-making process conditions in the transientpaper-making process condition changing period by an unestablishedmethod. Although the paper-making process condition control can beaccomplished successfully in a comparatively short time, thepaper-making process condition control takes a comparatively long timein most cases under the existing circumstances

The mode of drying of the web while the web is being dried by thesteam-heated drums of the predrying section and the afterdrying sectioncan be predicted by simulation using an appropriate model of paperdrying, and the pressure of steam to be supplied to the steam-heateddrums necessary to dry the web of a new basis weight in a desiredmoisture content can be determined by calculating based on the resultsof simulation of the mode of paper drying. Methods of calculating steampressure on the basis of results of simulation are explained in thefollowing papers.

1. John A. Depoy, "Analog Computer Simulation of Paper Drying a WorkableModel", PULP AND PAPER OF CANADA, Vol. 73, No. 5, p. 67 (May, 1972)

2. Jeffery A. Hinds, et al., "The Dynamic Computer Simulation of PaperMachine Dryer", Tappi Journal, Vol. 66, No. 6, p. 79, (June, 1983)

3. A. H. Nissan, et al., "Heat Transfer and Water Removal in CylinderDrying", Tappi Journal, Vol. 43, No. 9 (Sept., 1960)

The known method of simulation using a model of paper drying, however,must repeat a convergent calculation to determine the temperatures ofthe steam-heated drums and hence takes several minutes to calculate thetemperatures of the steam-heated drums even if a high-speed computer (anEWS or the like) is used for the calculation. Accordingly, it isdifficult to practically apply the aforesaid methods of simulation tothe predictive calculation and the control of paper-making processconditions.

DISCLOSURE OF THE INVENTION

Accordingly, a principal object of the present invention is to provide areliable method of controlling the moisture content of a web, during apaper-making process, which is capable of reducing the time necessaryfor changing paper-making process conditions, i.e., the time necessaryfor changing the grade of a web product, to the least possible extent,and a control apparatus for carrying out the method.

Another object of the present invention is to provide a method ofcontrolling the moisture content of a web which is capable of reducingthe amount of substandard web in producing the web by a paper-makingprocess on a paper machine, and a control apparatus for carrying out themethod.

In accordance with a first aspect of the present invention, there isprovided a steady-state simulation method for simulating the moisturecontent of a web on a paper machine at a steady state during a paperdrying process in which a moist web, along with a canvas belt, is passedaround steam-heated drums of steam-heated drum drying sections of thepaper machine to obtain a dried web product. An apparatus for carryingout the steady-state simulation method is also provided.

When carrying out steady-state simulation, heat balance among thesteam-heated drums of the steam-heated drum sections, the web, and thecanvas belt is described by heat balance equations on an assumption thata temperature distribution in the circumference portion of therespective steam-heated drums is uniform, and the heat balance equationsare reduced to difference equations. Initial values for the elements ofthe difference equations are given, and the difference equations aresolved repeatedly at given intervals to determine a moisture contenttransition pattern with respect to a direction of travel of the web inthe paper machine through the calculation of the respective temperaturesof the steam-heated drums, the canvas belt and the web. The finalmoisture content indicated on the moisture content transition pattern iscompared with an actually measured moisture content to detect whether ornot the final moisture content is within a given allowance with respectto the actually measured moisture content. If the final moisture contentis outside the limits of the allowance, a web-to-ambient mass transfercoefficient is corrected, and another moisture content transitionpattern is calculated. This procedure is repeated until the finalmoisture content falls within the given allowable range.

In accordance with another aspect of the present invention, there isprovided an unsteady-state simulation method for simulating a moisturecontent of a web at an unsteady state in a paper making process in whicha moist web, along with a canvas belt, is passed around the steam-heateddrums of steam-heated drum drying sections to dry the web, and steampressure supplied to the steam-heated drums of the steam-heated drumdrying section of the paper machine is varied. An apparatus for carryingout the unsteady-state simulation method is also provided.

When carrying out unsteady-state simulation, the heat balance betweenthe steam-heated drums of the steam-heated drum section, the web, andthe canvas belt is described by heat balance equations on an assumptionthat a temperature distribution in a circumference portion of each ofthe respective steam-heated drums is uniform, and the heat balanceequations are reduced to difference equations. The difference equationsare solved repeatedly, taking into consideration response time of thetemperature of the steam-heated drum when a steam pressure is varied, ata given time period to determine a moisture content transition patternwith respect to a direction of travel of the web in the paper machine.

In accordance with a further aspect of the present invention, there isprovided a transient moisture content control method for adjusting amoisture content of a web product on a paper machine in which the web,along with a canvas belt, is passed around the steam-heated drums ofsteam-heated drum drying sections to dry the web to a desired moisturecontent by controlling the steam pressures of the steam-heated drumswhen a web product grade is changed from one grade to a different grade,and an apparatus for carrying out the transient moisture content controlmethod is also provided.

When carrying out the transient moisture content control method, heatbalance among the steam-heated drums of the steam-heated drum section,the web, and the canvas belt is described by heat balance equations onan assumption that a temperature distribution in the circumference ofeach of the steam-heated drums is uniform, and the heat balanceequations are reduced to difference equations. Initial values for theelements of the difference equations are given, and the differenceequations are solved to determine a moisture content transition patternwith respect to a direction of travel of the web in the paper machineand a desired moisture content transition pattern is determined. Atemporal steam pressure transition pattern is produced by varying thesteam pressure supplied to the steam-heated drums in a given time periodand the moisture content transition pattern is calculated repeatedlytaking into consideration an assumed time lag in the response of thetemperature of the steam-heated drums to make the moisture contenttransition pattern coincide substantially with a desired moisturecontent transition pattern. When changing the paper-making processconditions of the paper machine, i.e., when the web product grade ischanged from one to a different grade, steam pressure for thesteam-heated drums is regulated on the basis of the steam pressuretransition pattern.

As mentioned above, according to the present invention, the temperaturesof the steam-heated drums are calculated by using the heat balanceequations describing the heat balance among the web, the steam-heateddrum and the canvas belt, on an approximate assumption that atemperature in the circumference of each steam-heated drum is fixed,i.e., an assumption that there is no temperature differential amongevery portions of the circumference of each steam-heated drums.Consequently, the above-mentioned calculation can be quicklyaccomplished.

BRIEF DESCRIPTION OF THE DRAWINGS

The above and other objects, features and advantages of the presentinvention will be described with reference to the accompanying drawings,in which:

FIG. 1 is a schematic perspective view of a paper machine for carryingout the present invention;

FIG. 2 is a block diagram of a paper machine incorporating the presentinvention therein;

FIG. 3 is an enlarged block diagram of the left half section of thepaper machine of FIG. 2 on the left side of division line D--D in FIG.2;

FIG. 4 is an enlarged block diagram of the right half section of thepaper machine of FIG. 2 on the right side of division line D--D in FIG.2;

FIG. 5 is a fragmentary side view of a drying section included in apaper machine;

FIG. 6 is a typical view of a hot plate model equivalent to the dryingsection of FIG. 5;

FIG. 7 is a flow chart of a steady-state simulation method in accordancewith the present invention;

FIG. 8 is a typical view for assistance in explaining the flow chart ofFIG. 7;

FIG. 9A is a graph showing a moisture content transition patternobtained by the steady-state simulation method of FIG. 7;

FIG. 9B is a diagram showing calculated results obtained by applying thesteady-state simulation method of the present invention to a practicalprocess;

FIG. 10 is a flow chart of a unsteady-state simulation method inaccordance with the present invention;

FIG. 11 is a three-dimensional graph showing, by way of example, theprogress of the unsteady-state simulation method of the presentinvention;

FIG. 12 is a diagrammatic view illustrating calculation to be performedby the unsteady-state simulation method of the present invention;

FIG. 13 is part of a flow chart of a moisture content control procedureto be carried out when changing paper-making process conditions;

FIG. 14 is another part of the flow chart of the moisture contentcontrol procedure continuous with the part shown in FIG. 13; and

FIG. 15 is a time diagram for assistance in explaining the flow chartsof FIGS. 13 and 14.

BEST MODE OF CARRYING OUT THE INVENTION

A paper-making process condition control apparatus according to apreferred embodiment of the present invention will be describedhereinafter.

FIG. 1 shows a representative paper machine, and FIG. 2 is a blockdiagram of the paper machine provided with a paper-making processcondition control apparatus embodying the present invention.

FIGS. 3 and 4 are enlarged fragmentary views of the paper machine ofFIG. 2, showing the left half section of the paper machine of FIG. 2 onthe left side of division line D--D in FIG. 2, and the right halfsection of the same paper machine on the right side of division lineD--D, respectively.

Referring to FIGS. 1 to 4, the paper machine has a wire section 10, apress section 12, a predrying section 14, a sizing section 16 and anafterdrying section 18.

The wire section 10 comprises an endless wire belt 10a wound around adrive roller 10b and a plurality of guide rollers 10c properly arrangedrelative to the drive roller 10b. The drive roller 10b is driven forrotation by an appropriate drive motor, not shown, to turn the wire belt10a so that the upper side of the endless wire belt 10a moves in thedirection of the arrows A shown in FIGS. 1, 2 and 3. A stock inlet unit20 is disposed at the receiving end of the endless wire belt 10a todischarge pulp slurry, i.e. paper stock, onto the upper side of theendless wire belt 10a. The pulp slurry is drained of water on the upperside of the endless wire belt 10a to form a web WE on the upper side ofthe endless wire belt 10a (FIGS. 1, 2 and 3). The water drained from thepulp slurry to form the web WE is called white water containing pulp ina low concentration. The white water is collected through a trough 22(FIGS. 2 and 3) extended under the wire section 10 in a white water pit24. The white water pit 24 is connected to the stock inlet unit 20 by aline 26 provided with an appropriate pump 28. A pulp supply line 32 hasone end connected to a pulp supply pipe unit 30 and the other endconnected to the line 26 at a position between the white water pit 24and the pump 28. The pulp supply line 32 is provided with an appropriatevalve 34. The opening of the valve 34 is regulated while the pump 28 isin operation to regulate the pulp concentration of the pulp slurrysupplied to the stock inlet unit 20.

The web "WE" formed in the wire section 10 is further drained of waterin the press section 12 to a moisture content on the order of 60%.Subsequently, the web "WE" is delivered to the predrying section 14. Thepredrying section 14 has an arrangement of a plurality of steam-heateddrums 14a heated by steam supplied thereto. The web "WE" is passedsequentially through the steam-heated drums 14a of the predrying section14 while being in close contact therewith to dry the web "WE" in apredetermined moisture content. Then, the web "WE" is subjected to asizing process in the sizing section 16, and the sized web "WE" istransferred to the afterdrying section 18. The afterdrying section 18 issubstantially the same in construction as the predrying section 14. Theweb "WE" is dried in a predetermined moisture content while the same ispassed through the afterdrying section 18. The web "WE" thus dried bythe afterdrying section 18 is taken up in a web roll 36.

The drying section 14 (18) will be described in detail with reference toFIG. 5.

An endless canvas belt 14b (18b) is passed around steam-heated drums 14a(18a), and the web "WE" is passed along with the canvas belt 14b (18b)through the steam-heated drums 14a (18a). In the example shown in FIG.5, the drying section 14 (18) has both a single-canvas drying structure,i.e., a structure on the left side in FIG. 5, and a double-canvas dryingstructure, i.e., a structure on the right side in FIG. 5.

In FIG. 5, the arrows marked on the steam-heated drums 14a (18a)indicates the respective directions of rotation of the correspondingsteam-heated drums 14a (18a).

In FIG. 1, the number of the steam-heated drums 14a of the predryingsection 14 is twenty for convenience sake, the predrying section 14 maybe provided with more than twenty steam-heated rollers. In thisembodiment, the steam-heated drums 14a are divided into those of a firstdrying unit 14₁, those of a second drying unit 14₂ and those of a thirddrying unit 14₃ as shown in FIGS. 2, 3 and 4. A common steam supplyheader 38₁ and a common drain header 40₁ are connected to thesteam-heated drums 14a of the first drying unit 14₁. Similarly, commonsteam supply headers 38₂ and 38₃, and common drain headers 40₂ and 40₃are connected to the steam-heated drums 14a of the second drying unit14₂ and the third drying unit 14₃, respectively. The steam-heated drums18a of the afterdrying section 18 are divided into those of a firstdrying unit 18₁ and a second drying unit 18₂.

A common steam supply header 42₁ and a common drain header 44₁ areconnected to the steam-heated drums 18a of the first drying unit 18₁and, similarly, a common steam supply header 42₂ and a common drainheader 44₂ are connected to the steam-heated drums 18a of the seconddrying unit 18₂.

As best shown in FIGS. 3 and 4, lines 46₁, 46₂ and 46₃ connected to thesteam supply headers 38₁, 38₂ and 38₃, respectively, are connected to amain steam supply line 48, which, in turn, is connected to a steamgenerator, not shown. The lines 46₁, 46₂ and 46₃ are provided withvalves 48₁, 48₂ and 48₃, and valve controllers 50₁, 50₂ and 50₃ areincorporated into the valves 48₁, 48₂ and 48₃, respectively. Adifferential pressure sensor 52 for detecting the difference in steampressure between the steam supply headers 38₁ and 38₂ is provided in aline having one and the other end connected to the steam supply headers38₁ and 38₂. The differential pressure sensor 52 is connected to thevalve controller 50₁. Similarly, a differential pressure sensor 54 fordetecting the difference in steam pressure between the steam supplyheaders 38₂ and 38₃ is provided in a line having one and the other endconnected to the steam supply headers 38₂ and 38₃. The differentialpressure sensor 54 is connected to the valve controller 50₂. A pressuresensor 56 is connected to the steam supply header 38₃ to detect thesteam pressure of the steam supply header 38₃. The pressure sensor 56 isconnected to the valve controller 50₃. Lines 58₁ and 58₂, connected tothe steam supply headers 42₁ and 42₂, respectively, are connected to amain steam supply line 60, which, in turn, is connected to the steamgenerator, not shown. The lines 58₁ and 58₂ are provided with valves 62₁and 62₂, and valve controllers 64₁ and 64₂ are incorporated into thevalves 62₁ and 62₂, respectively. A differential pressure sensor 66 fordetecting the difference in steam pressure between the steam supplyheader 42₁ and 42₂ is provided in a line having one end connected to thesteam supply headers 42₁ and the other end connected to the steam supplyheader 42₂. The differential pressure sensor 66 is connected to thevalve controller 64₁. A pressure sensor 68 is connected to the steamsupply header 42₂ to detect the pressure of the steam supply header 42₂.The pressure sensor 68 is connected to the valve controller 64₂.

A line 70₁ extending from the drain header 40₁ is connected to a flashtank 72₁. Similarly, lines 70₂ and 70₃ extending from the drain headers40₂ and 40₃, respectively, are connected to flash tanks 72₂ and 72₃,respectively.

As best shown in FIGS. 3 and 4, the flash tanks 72₁, 72₂ and 72₃ areconnected in series by lines 74 and 76. The flash tank 72₁ is connectedto a drain pump 80 by a line 78. The flash tank 72₂ is connected to thesteam supply header 38₁ by a line 82, and the flash tank 72₃ isconnected to the steam supply header 38 by a line 84. A line 86extending from the drain header 44₁ is connected to the flash tank 72₃.A line 88 extending from the drain header 44₂ is connected to a flashtank 90. The flash tank 90 is connected to the steam supply header 42₁by a line 92.

In the paper machine, the basis weight and the moisture content of theweb must be measured at positions just behind the predrying section andthe afterdrying section, and pulp slurry discharge rate at which thepulp slurry is discharged into the wire section, the steam pressure forthe steam-heated drums, and web speed must be controlled on the basis ofthe measured data. As mentioned above, these operations can be achievedby incorporating a well-known BM measuring system into the papermachine.

The BM measuring system comprises a first detecting unit 94 disposedjust behind the predrying section 14, a second detecting unit 96disposed just behind the afterdrying section 18, and a BM control unit98 for processing the detection data provided by the detecting units 94and 96 and for controlling the operations of the paper machine.

The first detecting unit 94 measures the basis weight and the moisturecontent of the web "WE" immediately after the web "WE" has been passedthrough the predrying section 14, and the second detecting unit 96measures the basis weight and the moisture content of the web "WE"immediately after the web "WE" has passed through the afterdryingsection 18. As can be seen from FIGS. 3 and 4, the valve 34 provided forthe pulp supply pipe unit 30 is connected to the BM control unit 98, andthe opening of the valve 34 is adjustably changed by a control signalprovided by the BM control unit 98 to control the pulp concentration ofthe pulp slurry supplied to the stock inlet unit 20; that is, the BMcontrol unit 98 regulates the opening of the valve 34 to control thebasis weight of the web "WE". The BM control unit 98 sends a controlsignal to the drive motor for driving the drive roller 10b for drivingthe endless wire belt 10a of the wire section 10 and to control the webspeed. The controllers 50₁, 50₂ and 50₃ associated with the first dryingunit 14₁, the second drying unit 14₂ and the third drying unit 14₃ ofthe predrying section 14, and the controllers 64₁ and 64₂ associatedwith the first drying unit 18₁ and the second drying unit 18₂ of theafterdrying section 18 are connected to the BM control unit 98. The BMcontrol unit 98 sends control signals to the controllers 50₁, 50₂, 50₃,64₁ and 64₂ to control the steam pressures of the steam-heated drums 14aand 18a by opening and closing the corresponding valves.

The controllers 50₁, 50₂, 50₃, 64₁ and 64₂ are controlled on the basisof steam pressure data provided by the corresponding sensors 52, 54, 56,66 and 68, respectively.

In short, the BM control unit 98 processes the detection data (basisweight and the moisture content of the web) provided by the firstdetecting unit 94 and the second detecting unit 96, and controls thepulp slurry discharge rate at which the pulp slurry is discharged intothe wire section 10 and the steam pressures of the steam-heated drums14a and 18a of the drying units 14₁, 14₂, 14₃, 18₁ and 18₂, on the basisof data obtained by processing the detection data, to produce a web of apredetermined quality.

The foregoing paper machine and the control procedure for controllingthe operations of the paper machine are well-known. The presentinvention provides a paper-making process condition control apparatus,i.e., a web product grade control apparatus, capable of controlling sucha paper machine so that the paper machine is able to accomplish a gradechanging operation of a web product quickly and in a short time.

A paper-making process condition apparatus or a grade change controlapparatus in accordance with the present invention uses a hot platemodel as shown in FIG. 6, which is equivalent to the drying sectionshown in FIG. 5, for controlling the web product grade changingoperation of the paper machine. In FIG. 5, the web WE is dried by thesteam-heated drums 14a (18a) as the same is passed around thesteam-heated drums 14a (18a) along with the canvas belt 14b (18b), whichis equivalent to drying the web "WE" as the same is passed through apath defined by hot plates 14a' (18a') fixedly disposed at givenintervals and canvas sheets 14b' (18b') properly combined with the hotplates 14a' (18') as shown in FIG. 6. In short, segments in FIG. 5 inwhich heat is transferred from the steam-heated drums 14a (18a) throughthe canvas belt 14b (18b) to the web "WE" corresponds to segment in FIG.6 in which heat is transferred from the hot plates 14a' (18a') throughthe canvas sheets 14b' (18b') to the web "WE", and segments in FIG. 5 inwhich heat is transferred directly from the steam-heated drums 14a (18a)to the web "WE" corresponds to segments in FIG. 6 in which heat istransferred directly from the hot plates 14a' (18a') to the web "WE".Sections in which no heat is transferred from the hot plates 14a' (18a')to the web "WE" are called free-run segments. In this example, thefree-run segments include those in which the web "WE" and the canvassheet 14b' (18b') are superposed and those in which the web "WE" travelsalone. The arrows in FIG. 6 indicate mode of evaporation of moisturefrom the web "WE".

Heat balances existing in the steam-heated drum 14a' (18a'), the canvasbelt 14b (18b) and the web "WE" are expressed by the followingequations.

Steam-heated Drum:

    (L.sub.D ·ρ.sub.D ·C.sub.D)·dT.sub.1 /dt= h.sub.s ·(T.sub.S -T.sub.1)-h.sub.DW ·(T.sub.1 -T.sub.2)!                                                (1)

Web:

    (L.sub.W·ρ.sub.W ·C.sub.W)·dT.sub.2 /dt= h.sub.DW ·T.sub.1 -(h.sub.DW +h.sub.WF)·T.sub.2 +h.sub.WF ·T.sub.3 -V·K·(P.sub.W -P.sub.ad)·H!                                    (2)

Canvas Sheet:

    (L.sub.F ·ρ.sub.F ·C.sub.F)·dT.sub.3 /dt= h.sub.WF ·T.sub.2 -(h.sub.WF +h.sub.a)·T.sub.3 +h.sub.a ·T.sub.a !                              (3)

Parameters used in Equations (1), (2) and (3) are as shown below.

L_(D) : Wall thickness of heated drums (m)

L_(W) : Thickness of web (m)

L_(F) : Thickness of canvas (m)

T_(S) : Steam temperature in heated drum (°C.)

T_(a) : Air temperature (°C.)

T₁ : Representative temperature of drum (°C.)

T₂ : Representative temperature of web (°C.)

T₃ : Representative temperature of canvas (°C.)

C_(D) : Specific heat of drum (kcal/kg·°C.)

C_(w) : Specific heat of web (kcal/kg·°C.)

C_(F) : Specific heat of canvas (kcal/kg·°C.)

ρ_(D) : Density of drum (kg/m³)

ρ_(W) : Density of web (kg/m³)

ρ_(F) : Density of canvas (kg/m)

h_(S) : Heat transfer coefficient between steam in drum and the innersurface of drum (kcal/m² ·sec·°C.)

h_(Dw) : Heat transfer coefficient between the outer surface of drum andweb (kcal/m·sec·°C.)

h_(wF) : Heat transfer coefficient between web and canvas (kcal/m²·sec·°C.)

h_(a) : Heat transfer coefficient between canvas and the atmosphere(kcal/m² ·sec·°C.)

V: Evaporative factor (-)

Evaporative factor is a nondimensional parameter, such as constant-ratedrying correction factor or a falling-rate drying correction factor,indicating evaporation rate dependent on the moisture content of theweb.

K: Web-to-ambient mass transfer coefficient (H₂ O kg/kg·Hr·)

P_(W) : Saturation vapor pressure of water at web temperature (kg/m²)

P_(ad) : Saturation vapor pressure of water at the wet-bulb temperatureof the ambient air (kg/m²)

H : Heat of evaporation of water (kcal/H₂ O)

The above Equation (1) is based on a condition that the rate of changeof heat stored in the drum (the drum material) with time is equal to thedifference between heat that flows from the steam in the drum to thedrum material and the heat that flows out from the drum material, whichapplies also to Equations (2) and (3).

Incidentally, the temperature of an optional point on the circumferenceof the steam-heated drum of a steam dryer drops when the point comesinto contact with the web and rises after the point has separated fromthe web.

When determining the temperature of a drum by conventional simulation,an initial value is assigned to such an optional point, temperaturevariations are calculated at a given period, the calculated temperatureof the point after the drum has turned one full turn is compared withthe initial value, the same calculations are repeated using thecalculated temperature as an initial value, and it is decided that thetemperature of the drum is obtained upon the coincidence of thecalculated temperature and the initial value. The conventionalsimulation using such a convergent calculation takes a very long time,and several minutes is necessary for calculating the temperatures of allthe steam-heated drums even if a high-speed electronic computer, such asan EWS, is used. Accordingly, it has been difficult to estimate themoisture content of the web and to achieve paper-making processcondition control (a web product grade change control) in an on-linemode by using the conventional method of simulation.

A method of simulation of moisture content in accordance with thepresent invention and web product grade change control using moisturecontent determined by the method of simulation is based on an assumptionthat a temperature distribution in the circumference of a steam-heateddrum is substantially uniform and the temperature difference betweenpoints on the circumference of the steam-heated drum is negligible.

According to the present invention, it is assumed that the temperaturevariation of a point on the circumference portion of the steam-heateddrum is very small during the normal operation of the steam-heated drumeven if the circumference has a section in contact with the web and asection not in contact with the web because the steam-heated drumrotates at a high rotating speed. The temperature difference between theabove-mentioned two sections estimated by the conventional simulation ofthe steam-heated drum was about 1° C. or below and the temperatures ofpoints on the same circumference of the steam-heated drum differscarcely from each other. The simulation of the moisture content of theweb in accordance with the present invention and paper-making processcondition control using the results of simulation are based on thefollowing assumptions.

dT₁ /dx=0

where T₁ is the temperature of the drum, x is the distance of travel ofa point on the circumference of the drum, dx=d(V·t), V is the surfacespeed of the drum, and t is time.

It is assumed for the present time that "V" is constant. Therefore,

    dT.sub.1 /d(V·t)=(1/V)·(dT.sub.1 /dt)=0

    dT.sub.1 /dt=0

Therefore, equation (1) is:

    (L.sub.D ·ρ.sub.D ·C.sub.W)·dT.sub.1 /dt= h.sub.S ·(T.sub.S -T.sub.1) -h.sub.DW·(T.sub.1 -T.sub.2)!=0

and then,

    T.sub.1 =(h.sub.S ·T.sub.S +h.sub.DW·T)/(h.sub.S +h.sub.DW)                                                (4)

Heat balance equation (2) is rewritten in a forward difference equation:

    dT.sub.2 /dt=(T.sub.2(Now) -T.sub.2(OLD) /Δt T.sub.2(NOW) =T.sub.2(OLD) + Δt/(L.sub.W ·ρ.sub.W ·C.sub.W) !· h.sub.DW·T.sub.1(NOW) -(h.sub.DW +h.sub.DF)·T.sub.2(OLD) +h.sub.WF·T.sub.3(NOW) -V·K·(P.sub.W -P.sub.ad)·H!    (5)

and heat balance equation (3) is rewritten in a forward differenceequation:

    dT.sub.3 /dt=(T.sub.3(Now)-T.sub.3(OLD))/Δt T.sub.3(NOW) =T.sub.3(OLD) + Δt/(L.sub.F ·ρ.sub.F ·C.sub.F !· h.sub.WF ·T.sub.2(NOW) -(h.sub.WF +h.sub.a)·T.sub.3(OLD) +h.sub.a ·T.sub.a !(6)

where the "NOW" is a subscript indicating the value of the correspondingvariable after a time Δt from the time "OLD".

As mentioned above, since the present invention is based on anassumption: dT₁ /dt=0, a term in Equation (1), indicating the effect ofthe heat capacity of the drum, i.e., (L_(D) ·ρ_(D)·C_(D)) is neglected.

Although no significant problem arises in the calculation of conditionseven if the term, (L_(D) ·ρ_(D) ·C_(D)) is neglected when calculatingconditions in a steady state, the variation of the temperature of thedrum cannot be expressed only by the aforesaid model in the dynamicsimulation of the unsteady state in which the temperature of the drumvaries with a time lag when the steam pressure for the drum is changedor the web speed is changed when changing the web product grade. Sincethe effect of the term, (L_(D) ·ρ_(D) ·C_(D)) is not disregardable, theaforesaid problem is solved by combining a model expressed by afirst-order lag function, which is shown below, with the aforesaid modelto calculate the temperature of steam so that the drum pressure variesasymptotically with a time lag when the pressure of steam is changed inthe simulation of a unsteady state.

    T.sub.S(NOW) =f(P.sub.(OLD) + 1-exp{(-(t-t.sub.(DEAD))}/τ.sub.0 !· f(P.sub.(NOW))-f(P.sub.(OLD))!                (7)

where t.sub.(DEAD) is a simple time lag in response, τ₀ is time constantand f is reduction function for converting a pressure of steam to acorresponding temperature.

A model in accordance with the present invention is based on anassumption that the amount of moisture evaporating from the web isapproximately proportional to a difference between saturated vaporpressure at a temperature of the web and that at a temperature of theambient air as expressed by an equation shown below. However, a moreprecise model may be used. For example, more precisely, the rate ofevaporation of moisture from the web is dependent on the differencebetween water vapor concentration at the temperature of the web and thatat the temperature of the ambient air. The moisture content of the webmay be calculated by using such a more precise model.

    W=V·K·(P.sub.W -P.sub.ad) Δt       (8)

where W is the amount of moisture (H₂ O kg/cm²) evaporated from the webinto the ambient air, Δt is a time for which the web is subjected todrying process, i.e., the time interval between calculation cycles.Equation (8) is part of Equations (2) and (5).

The moisture content of the web is updated on the basis of calculatedvalues calculated by using the foregoing equations every time thecalculation cycle is completed by using:

    M.sub.(NOW) =M.sub.(OLD) -Ψ(W)                         (9)

where M is the moisture content of the web, Ψ(W) is a reduction functionfor reducing an amount of moisture into a moisture content of the web.

As shown in FIG. 3 and 4, the paper-making process condition controlapparatus according to the present invention includes a high-speedmicrocomputer 100 operatively connected to the BM control unit 98 of theconventional BM measuring system, and includes a manually input means,e.g., a keyboard 102, and an appropriate display unit, e.g., a CRT (notshown).

In accordance with the present invention, the steady state operation ofthe paper machine is simulated by a simulation routine shown in FIG. 7.

In step 701, the microcomputer 100 reads process conditions includingthe web speed, the basis weight and the desired moisture content of theweb, i.e., data provided by the detecting units 94 and 96, steampressures of steam in the steam-heated drums of the drying units 14₁,14₂, 14₃, 18₁ and 18₂, data representing the moisture content of the webat the entrance of the drying section 14, the air temperatures of thedrying sections 14 and 18, and such detected by sensors, not shown. Anoptional web-to-ambient mass transfer coefficient K is determined instep 702, and the steam pressures in the drying units 14₁, 14₂, 14₃, 18₁and 18₂ are converted into corresponding steam pressures in step 703.

In steps 704, 705 and 706, the temperature of the web "WE", thetemperatures of the canvas belts 14b and 18b, and the temperatures ofthe steam-heated drums 14a and 18b at positions in the drying units 14₁,14₂, 14₃, 18₁ and 18₂ are calculated by using equations (5), (6) and(4), respectively. In step 707, the amount of evaporation from the web"WE" is calculated by using the calculated temperatures and Equation(8), and then the moisture content of the web "WE" is calculated byusing Equation (9) in step 708.

In step 709, a query is made to see whether the moisture content of theweb WE in the drying units 14₁, 14₂, 14₃, 18₁ and 18₂ of all the dryingsections has been calculated at the given time period. Morespecifically, as shown in FIG. 8, the moisture content of the web "WE"is calculated at an infinitesimal time period Δt, e.g., approximately 20msec, by using the model shown in FIG. 6. A moisture content transitionpattern as shown in FIG. 9 is obtained when the calculation cycle isrepeated at the time period Δt for all the drying units 14₁, 14₂, 14₃,18₁ and 18₂.

In step 710, moisture content data on the aforesaid calculated moisturecontent transition pattern are compared with measured moisture contentdata. A moisture content PM (FIG. 9A) of the web "WE" immediately afterthe web "WE" has passed through the predrying section 14 is comparedwith an actually measured moisture content of the web "WE" measured bythe first detecting unit 94 of the BM measuring system, and a moisturecontent PM (FIG. 9A) of the web "WE" immediately after the web "WE" haspassed through the afterdrying section 18 is compared with a measuredmoisture content of the web "WE" measured by the second detecting unit96 of the BM measuring system. If the difference determined by thecomparison is beyond an allowable range, the web-to-ambient masstransfer coefficient K is corrected in step 711. Then, the simulationusing the model shown in FIG. 6 is repeated. If the differencedetermined by the comparison is within the allowable range, the resultsof simulation are displayed on the CRT of the microcomputer 100 in step712.

Generally, a time on the order of five minutes is necessary toaccomplish the conventional steady-state simulation method requiring theconvergent calculation needs, however, the present invention is capableof accomplishing the steady-state simulation method in about one to twoseconds.

FIG. 9B is a diagram showing calculated results obtained by applying thesteady-state simulation method of the present invention to a practicalprocess.

Calculations for obtaining the calculated results shown in FIG. 9B werecarried out under the following conditions.

Paper-making speed: 851 m/min

Basis weight (before sizing): 61.0 g/m²

Basis weight (after sizing): 68.0 g/m²

Size (pigment) pickup: 7.08 g/m²

Steam pressure for predrying section

Third drying unit: 3.5 kg/cm² ·abs.

Second drying unit: 2.9 kg/cm² ·abs.

First drying unit: 2.3 kg/cm² ·abs.

Steam pressure for afterdrying section

Second drying unit: 2.4 kg/cm² ·abs.

First drying unit: 1.6 kg/cm² ·abs.

In accordance with the present invention, an unsteady-state simulationroutine as shown in FIG. 10 is executed to simulate an unsteady state,such as a state where the paper-making process conditions of the papermachine (basis weight, web speed and such) are changed. The simulationof such an unsteady state corresponds to changing a moisture contenttransition pattern MP₁ shown in FIG. 11 obtained by simulation at a timepoint during the operation of the paper machine in a steady state to aweb moisture content transition pattern MP₂ shown in FIG. 11.

In step 1001, changing modes of paper-making process conditionsincluding steam pressures, web speeds and basis weights for the dryingunits 14₁, 14₂, 14₃, 18₁ and 18₂ are determined. The changing modes areselectively determined according to variations in the basis weight andthe web speed.

In step 1002, the microcomputer 100 reads process conditions includingthe web speed, the basis weight and the desired moisture content of theweb, i.e., data provided by the detecting units 94 and 96, the pressuresof steam in the steam-heated drums of the drying units 14₁, 14₂, 14₃,18₁ and 18₂, data representing the moisture content of the web at theentrance of the drying section 14, the air temperatures in the dryingsections 14 and 18, and such, in a calculation cycle.

In step 1003, the steam pressures of steam in the drying units 14₁, 14₂,14₃, 18₁ and 18₂ are converted into corresponding steam temperaturestaking into consideration time lags, in response of the steamtemperatures, in the drying units on the basis of Equation (7).

In step 1004, the steady-state simulation similar to that shown in FIG.7 is implemented, and a query is made in step 1005 to see whethercalculations for the entire simulation time have been completed. If theresponse to query in step 1005 is negative, a given calculation timeperiod is advanced by ΔT (FIG. 11) in step 1006, and the simulation isrepeated. More concretely, suppose, for example, that the distributionsof the steam-heated drum temperatures in the drying sections are Td₁ andTd₂, the distributions of the canvas belt temperatures are TC₁ to TC₆,the distributions of the web temperatures are TW₁ to TW₆, and thedistributions of the web moisture contents are M₁ to M₆ as shown in FIG.12. Then, the unsteady-state simulation is carried out using those dataas initial values.

Then, the distributions Td₁ and Td₂ of the steam-heated drumtemperatures change to Td₁ ' and Td₂ ', the distributions Tc₁ to Tc₆ ofthe canvas belt temperatures change to Tc₁ ' to TC₆ ', the distributionsTw₁ to Tw₆ of the web temperatures change to TW₁ ' to Tw₆ ', and thedistributions M₁ to M₆ of the web moisture contents change to M₁ ' to M₆'.

Subsequently, the distributions Tc₁ ' to Tc₇ 'of the canvastemperatures, the distributions Tw₁ to Tw₇ of the web temperatures, thedistributions Tw₁ ' to Tw₇ 'of the web moisture contents, and thedistributions M₁ ' to M₇ ' are shifted by one data relative to thedistributions Td₁ ' and Td₂ ' of the steam-heated drums, and theunsteady-state simulation is executed again using these data as initialvalues. Consequently, the distributions Td₁ ' and Td₂ ' of thesteam-heated drum temperatures change to distributions Td₁ " and Td₂ ",the distributions Tc₁ ' to Tc₇ ' of the canvas belt temperature changeto Tc₁ " to Tc₇ ", distributions Tw₁ ' to Tw₇ ' of the web temperatureschange to Tw₁ " to Tw₇ " and the distributions M₁ ' to M₇ ' of the webmoisture contents change to M₁ " to M₇ ". Thus, the web moisture contenttransition pattern MP₁ in the drying sections is modified at a timeperiod of ΔT toward the web moisture content pattern MP₂ by simulation.

Whereas the conventional unsteady-state simulation method requiringconvergent calculations takes about one to two hours to accomplish theunsteady-state simulation, the present invention is able to accomplishthe unsteady-state simulation in about one to two minutes.

The operation of the present invention for controlling the moisturecontent of the web based on the foregoing steady-state simulation andthe unsteady-state simulation will be described with reference to a flowchart shown in FIG. 13.

In step 1301, the microcomputer 100 sets paper-making process conditionsincluding a new basis weight, a new web speed, a new final moisturecontent of the web and such. The microcomputer 100 reads the presentvalues of paper-making process variables of the paper machine from theBM measuring system in step 1302, and then the steady-state simulation(FIG. 7) is carried out on the basis of the present values of theprocess variables in step 1303 to determine the web-to-ambient masstransfer coefficient K.

In step 1304, the new values of the process variables including gradenumber, web speed, basis weight, moisture content and such after thechange of the paper-making process conditions are read, and thenpaper-making process time is determined in step 1305 on the basis of thepaper-making process conditions; that is, modes of transition with timeof process variables including web speed and basis weight are determinedon the basis of the paper-making process conditions.

Desired moisture contents of the web "WE" immediately after the web haspassed through the drying units 14₁, 14₂, 14₃, 18₁ and 18₂ after thechange of the paper-making process conditions, i.e., after the change ofthe web product grade, are determined in step 1307. The desired moisturecontents are, for example, PT_(e) M₁, PT_(e) M₂, PT_(e) M₃, AT_(e) M₁and AT_(e) M₂ as indicated in FIG. 11.

In step 1308, transition profiles ptm₁, ptm₂, ptm₃, atm₁ and atm₂ (FIG.11) of the target moisture contents of the web "WE" in the drying units14₁, 14₂, 14₃, 18₁ and 18₂ during the change of the paper-making processconditions are determined. Subsequently, appropriate allowances for thedesired moisture contents are determined from the above-mentioned targetmoisture contents in step 1309.

Steam pressures for the drying units 14₁, 14₂, 14₃, 18₁ and 18₂ are setin step 1310. Preferably, the set steam pressures are equal to thoseread as initial values in step 1301, i.e., the steam pressures used inthe preceding paper-making process. The unsteady-state simulation (FIG.10) is performed sequentially for the drying units at the time ofsimulation carried out during a web product grade change to determinemoisture contents transition patterns in which the moisture content ofthe web at the respective exits of the drying units change. Then, instep 1312, moisture contents specified by the moisture contenttransition patterns are compared with the corresponding desired moisturecontents. If the difference between the moisture content specified bythe moisture content transition pattern and the corresponding desiredmoisture content is outside an allowance, fine steam pressure adjustmentis carried out for the corresponding drying unit in step 1313, and thenthe unsteady-state simulation is repeated.

A method of fine steam pressure adjustment to be carried out in step1313 will be described below. The increase of the moisture content ofsome region of the web beyond the desired moisture content signifies anexcessively low steam pressure. When it is thus found that the currentsteam pressure is excessively low, the simulation is repeated afteradding a given steam pressure correction Δp to the current set steampressure. If the correction of the steam pressure reduces the moisturecontent of the same region of the web below the desired moisturecontent, it is considered that the steam pressure correction Δp isexcessively large. Therefore, half the steam pressure correction Δp,i.e., Δp/2, is subtracted from the new set steam pressure, and then thesimulation is repeated. Thus, the steam pressure correction is reducedby half when the moisture content deviates in the opposite side from thedesired moisture content in order that the calculated result fall withinthe allowable range for the desired moisture content, whereby anappropriate steam pressure can be efficiently determined.

If it is found that the moisture content of the web is within theallowance for the desired moisture content in step 1312, step 1314 isexecuted to see whether the simulation has been completed for all thedrying units 14₁, 14₂, 14₃, 18₁ and 18₂. The simulation is repeated atthe time period Δt (FIG. 11) in the paper-making process conditionchange simulation time for the drying units.

After the completion of the simulation for all the drying units, part ofthe results of calculations, i.e., steam pressure transition patternsfor the drying units 14₁, 14₂, 14₃, 18₁ and 18₂ are stored as steampressure control patterns in the storage of the microcomputer 100 instep 1315.

FIG. 15 is a time diagram which illustrates modes of control of theprincipal process variables by the foregoing simulation by way ofexample. In this example, as is obvious from curves in the middlesection of FIG. 15, web speed is increased and basis weight is reduced.The moisture content transition patterns (shaded regions indicateallowable ranges) and steam pressure control patterns are showntypically in the lower section of FIG. 15. In FIG. 15, data concerningthe drying units of the afterdrying section 18 are omitted.

In step 1316, a query is made to see whether a paper-making processcondition change command has been given. The operator operates the inputmeans, such as the keyboard 102, to give the paper-making processcondition change command. When the paper-making process condition changecommand is given, the steam pressures for the drying units 14₁, 14₂,14₃, 18₁ and 18₂ are controlled according to steam pressure controlpatterns at a given control time period in step 1317 to control themoisture content of the web actually used during the paper-makingprocess condition change.

As can be seen from FIG. 11, the paper-making process condition changesimulation time corresponds to a time interval between the start and theend of the paper-making process condition change, i.e., the distancebetween the moisture content transition patterns MP₁ and MP₂. However,since a time necessary for adjusting the final moisture content to thedesired final moisture content must be allowed for, it is preferablethat the actual paper-making process condition change control time issomewhat longer than the paper-making process condition changesimulation time as shown in FIG. 15.

As is apparent from the foregoing description, according to the presentinvention, the steam pressure transition patterns for paper-makingprocess condition change are determined by simulation before thepaper-making process condition change is practiced, and the steampressures in the drying units are controlled according to the steampressure control patterns during operation for the paper-making processcondition change in a predetermined time to obtain a web having adesired moisture content.

Tables (I) and (II) show comparatively the predicted final steampressures of the steam-heated drums and final steam pressures reached bythe application of moisture content control method of the presentinvention for controlling the moisture content during the paper-makingprocess condition change to an actual paper-making process, and thosedetermined by calculation by the conventional method.

                  TABLE (I)                                                       ______________________________________                                        *3         *4        *5      *6 (kg/cm.sup.2 abs)                             (m/min)    (g/m.sup.2)                                                                             (%)          *7                                          No.  *1     *2     *1   *2   *1  *2  *1   *8   *9   *10                       ______________________________________                                        1    588    678    91.0 80.0 4.5 4.8 4.35 2.82 4.36 4.32                      2    716    507    68.6 94.1 2.4 3.0 3.53 7.23 3.28 3.58                      3    781    780    48.1 57.1 2.0 2.2 2.46 3.38 3.11 3.43                      4    847    847    53.8 49.0 2.4 2.4 3.58 3.40 3.09 2.98                      5    834    846    49.0 52.3 2.3 2.2 2.47 2.54 2.83 2.96                      ______________________________________                                         *1 Before grade change of web product                                         *2 After grade change of web product                                          *3 Web speed (m/min)                                                          *4 Basis weight (g/m.sup.2) before application of sizing agents               *5 Moisture content (%) before application of sizing agents                   *6 Final steam pressure (kg/cm.sup.2 · abs) in drums of three        predryer sections                                                             *7 Predicted value after grade change                                         *8 Conventional method                                                        *9 Method according to the invention                                          *10 Actual resultant value                                               

                  TABLE (II)                                                      ______________________________________                                        *11        *12       *13     *14 (kg/cm.sup.2 abs)                            (g/m.sup.2)                                                                              (g/m.sup.2)                                                                             (%)          *7                                          No.  *1     *2     *1   *2   *1  *2  *1   *8   *9   *10                       ______________________________________                                        1    14.0   15.1   105.1                                                                              95.1 5.2 5.2 2.87 0.46 2.80 2.78                      2    15.2   12.4   83.8 106.5                                                                              5.6 4.5 1.67 5.38 1.92 1.41                      3    11.7   11.9   59.8 69.0 4.9 5.4 1.69 3.13 1.33 1.64                      4    11.3   11.8   65.1 60.8 5.3 5.3 1.58 1.11 1.86 1.85                      5    2.8    2.7    51.8 55.0 5.0 4.4 1.52 1.73 1.89 1.66                      ______________________________________                                         *1 Before Grade Change                                                        *2 After Grade Change                                                         *7 Predicted Value After Grade Change                                         *8 Conventional method                                                        *9 Method according to the Invention                                          *10 Actual resultant value                                                    *11 Application Amount of Sizing Aqents                                       *12 Basis Weight after Application of Sizing Agents                           *13 Final Moisture Content                                                    *14 Final Steam Pressure in Drums of Five Afterdryer Sections            

As can be seen from Tables (I) and (II), the predicted values predictedby the method of the present invention agree satisfactorily withcorresponding final values as compared with the values calculated by theconventional values.

As is apparent from the foregoing description, the present invention isable to simulate the operating condition of the paper machine quickly ascompared with the conventional method and is able to adjust the moisturecontent of the web immediately after the web has passed through eachdrying section and the final moisture content of the web to desiredvalues, in a comparatively short time.

Thus, the present invention reduces the time necessary for changing thepaper-making process conditions, reduces the amount of waste webproduced during the paper-making process condition change andcontributes to the reduction in the cost of the product as well.

I claim:
 1. A method of on-line simulating a moisture content of a webproduct of a web at a steady state on a paper machine by using amicrocomputer, said method comprising the steps of:passing said web,along with a canvas belt, around each steam-heated drum of a pluralityof steam-heated drums of a steam web dryer to dry said web duringtraveling thereof; detecting, by detecting units, at least steampressure in each steam-heated drum of said plurality of steam-heateddrums, web basis weight, web traveling speed, and moisture content ofsaid web at a discharge end of said steam web dryer; describing a heatbalance, among all of each steam-heated drum of said plurality ofsteam-heated drums of said steam web dryer, said web, and said canvasbelt, by heat balance equations on an assumption that a temperaturedistribution in a circumferential portion of each steam-heated drum ofsaid plurality of steam-heated drums is uniform, and reducing said heatbalance equations to difference equations; determining a moisturecontent transition pattern over an entire drying section of said steamweb dryer in a direction of travel of said web by substituting giveninitial values for elements of said difference equations, and repeatedlysolving said difference equations at given times associated with travelof said web, by calculating respective temperatures of all of eachsteam-heated drum of said plurality of steam-heated drums, said canvasbelt and said web, along said direction of travel of said web; comparinga final moisture content indicated on said moisture content transitionpattern with said moisture content actually detected by said detectingunits; deciding whether said final moisture content indicated on saidmoisture content transition pattern is within a predetermined allowancewith respect to said actually detected moisture content; and correctinga web-to-ambient mass transfer coefficient if said final moisturecontent is not within said predetermined allowance, and repeatedlycalculating said moisture content transition pattern until said finalmoisture content falls within said predetermined allowance with respectto said actually detected moisture content to thereby obtain asteady-state moisture content transition pattern, said steady-statemoisture content transition pattern being indicated as an output ofsimulation.
 2. An apparatus for on-line simulating a moisture content ofa product of a web product of a web at a steady state on a paper machineby using a microcomputer, said apparatus comprising:means for passingsaid web, along with a canvas belt, around each steam-heated drum of aplurality of steam-heated drums of a steam web dryer to dry said webduring traveling thereof; a detecting means for detecting at least steampressure in each steam-heated drum of said plurality of steam-heateddrums, web basis weight, web traveling speed, and moisture content ofsaid web at a discharged end of said steam web dryer; a storage meansfor storing difference equations obtained by reducing heat balanceequations, describing a heat balance among all of each steam-heated drumof said plurality of steam-heated drums of said steam web dryer, saidweb, and said canvas belt, on an assumption that a temperaturedistribution in a circumferential portion of each steam-heated drum ofsaid plurality of steam-heated drums is uniform; a calculating meansboth for substituting given initial values for elements of saiddifference equations stored in said storage means, and for repeatedlysolving said difference equations at given times associated with travelof said web, to determine a moisture content transition pattern over adrying section of said steam web dryer in a direction of travel of saidweb through calculation of respective temperatures of all of eachsteam-heated drum of said plurality of steam-heated drums, said web andsaid canvas belt, along said direction of travel of said web; acomparing means for comparing a final moisture content indicated on saidmoisture content transition pattern with said moisture content of saidweb, actually detected at a discharged end of said steam web dryer bysaid detecting means; a deciding means for deciding whether said finalmoisture content indicated on said moisture content transition patternis within a given allowance with respect to said actually detectedmoisture content; and a means both for correcting a web-to-ambient masstransfer coefficient if said final moisture content is not within saidgiven allowance, and for repeatedly calculating said moisture contenttransition pattern until said final moisture content falls within saidgiven allowance to thereby obtain a steady-state moisture contenttransition pattern, said steady-state moisture content transitionpattern being indicated as an output of simulation.
 3. A method ofon-line simulating a moisture content of a product of a web product of aweb in an unsteady state on a paper machine by using a microcomputer,said method comprising the steps of:passing said web, along with acanvas belt, around each steam-heated drum of a plurality ofsteam-heated drums of a steam web dryer to dry said web during travelthereof; varying respective steam pressures of each steam-heated drum ofsaid plurality of steam-heated drums; describing a heat balance amongall of each steam-heated drum of said plurality of steam-heated drums ofsaid steam web dryer, said web, and said canvas belt, by heat balanceequations on an assumption that a temperature distribution in acircumference of each steam-heated drum of said plurality ofsteam-heated drums is uniform, and reducing said heat balance equationsto difference equations; and repeatedly calculating a moisture contenttransition pattern over an entire drying area within said steam webdryer in a direction of travel of said web varying with time at a giventime period by using both detected data of said steam pressure in eachsteam-heated drum of said plurality of steam-heated drums, said webbasis weight, said web traveling speed, and said moisture content ofsaid web at a discharge end of said steam web dryer, and said differenceequations, while taking into consideration a time lag in response of atemperature of each steam-heated drum of said plurality of steam-heateddrums to a variation of said steam pressure for each steam-heated drumof said plurality of steam-heated drums to correct errors attributableto said assumption, said calculated moisture content transition patternbeing indicated as an output of an unsteady state simulation.
 4. Anapparatus for on-line simulating a moisture content of a web product ofa web on a paper machine by using a microcomputer, said apparatuscomprising:means for passing said web, along with a canvas belt, aroundeach steam-heated drum of a plurality of steam-heated drums of a steamweb dryer to dry said web during travel thereof; a detecting means fordetecting at least steam pressure in each steam-heated drum of saidplurality of steam-heated drums, web basis weight, web traveling speed,and moisture content of said web at a discharged end of said steam webdryer; means for varying respective steam pressures of each steam-heateddrum of said plurality of steam-heated drums; a storage means forstoring difference equations obtained by reducing heat balance equationsdescribing a heat balance among all of each steam-heated drum of saidplurality of steam-heated drums of said steam web dryer, said web, andsaid canvas belt, on an assumption that a temperature distribution in acircumference of each steam-heated drum of said plurality ofsteam-heated drums is uniform; a calculating means for repeatedlycalculating a moisture content transition pattern with respect to adirection of travel of said web in said steam web dryer varying withtime at a given time period by using said difference equations, takinginto consideration a time lag in a response of a temperature of eachsteam-heated drum of said plurality of steam-heated drums to a variationof said steam pressure applied to each steam-heated drum of saidplurality of steam-heated drums to correct errors attributable to saidassumption; and means for indicating said moisture content transitionpattern as an output of an unsteady state simulation.
 5. A method ofadjusting and controlling a moisture content of a web product of a webon a paper machine by using a microcomputer, said method comprising thesteps of:passing said web, along with a canvas belt, around eachsteam-heated drum of a plurality of steam-heated drums forming aplurality of separate drying areas of a steam web dryer, to dry said webto a desired moisture content by controlling transition of a steampressure supplied to each steam-heated drum of said plurality ofsteam-heated drums when changing a grade of said web product on saidpaper machine; detecting, by detecting units, at least steam pressure ineach steam-heated drum of said plurality of steam-heated drums, webbasis weight, web traveling speed, and moisture content of said web atdischarge ends of said plurality of separate drying areas; describing aheat balance among all of each steam-heated drum of said plurality ofsteam-heated drums of said steam web dryer, said web, and said canvasbelt, by heat balance equations on an assumption that a temperaturedistribution in a circumference portion of each steam-heated drum ofsaid plurality of steam-heated drums is uniform, and reducing said heatbalance equations to difference equations; determining a moisturecontent transition pattern at a steady state in a direction of travel ofsaid web within said steam web dryer by substituting appropriate initialvalues for elements of said difference equations and repeatedly solvingsaid difference equations at given times associated with travel of saidweb until a final moisture content obtained from said moisture contenttransition pattern falls within a predetermined allowance with respectto said actually detected moisture content; setting a desired moisturecontent pattern for each of discharge ends of said plurality of dryingareas during predetermined times of changing grade of said web product,on a basis of said determined steady state moisture content transitionpattern while introducing paper making process conditions after changinggrade of said web product into said microcomputer; and obtaining amoisture content transition pattern at each of said discharge ends ofsaid plurality of drying areas in a direction of travel of said websduring times of changing grade of said web product from varying saidsteam pressure supplied to each steam-heated drum of said plurality ofsteam-heated drums at a given time period and repeatedly calculating, bysaid difference equations, said moisture content transition pattern at agiven time period, while taking into consideration an assumptive timelag in a response of a temperature of each steam-heated drum of saidplurality of steam-heated drums, and simultaneously producing anassociated temporal steam pressure transition pattern of eachsteam-heated drum of said plurality of steam-heated drums during timesof changing grade of said web product, in order to make said moisturecontent transition pattern at each of said discharge ends of saidplurality of drying areas during predetermined times of changing gradeof said web product coincide substantially with said desired moisturecontent pattern within a predetermined allowance; and changing saidsteam pressure supplied to each steam-heated drum of said plurality ofsteam-heated drums based upon said steam pressure transition patternwhen actually changing said grade of said web product on said papermachine.
 6. An apparatus for adjusting a moisture content of a webproduct of a web on a paper machine by using a microcomputer, saidapparatus comprising:means for passing said web, along with a canvasbelt, around each steam-heated drum of a plurality of steam-heated drumsforming a plurality of separate drying areas of a steam web dryer to drysaid web to a desired moisture content; a detecting means for detectingat least steam pressure in each steam-heated drum of said plurality ofsteam-heated drums, web basis weight, web traveling speed, and moisturecontent of said web at discharge ends of said plurality of separatedrying areas; means for controlling transition of a steam pressuresupplied to each steam-heated drum of said plurality of steam-heateddrums when changing said grade of said web product on said papermachine; a storage means for storing difference equations obtained byreducing heat balance equations describing a heat balance among all ofeach steam-heated drum of said plurality of steam-heated drums of saidsteam web dryer, said web, and said canvas belt, on an assumption that atemperature distribution in a circumference of each steam-heated drum ofsaid plurality of steam-heated drums is uniform; a calculating means forcalculating a moisture content transition pattern at a steady state in adirection of travel of said web within said steam web dryer bysubstituting appropriate initial values for elements of said differenceequations and repeatedly solving said difference equations at giventimes associated with travel of said web until a final moisture contentobtained from said moisture content transition pattern falls within apredetermined allowance with respect to said actually detected moisturecontent; means for introducing paper making process conditions afterchanging of said grade of said web product into said microcomputer; asetting means for setting a desired moisture content pattern for each ofsaid discharge ends of said plurality of drying areas duringpredetermined times of changing said grade of said web product, on abasis of said moisture content transition pattern at a steady state; acalculating means both for obtaining a moisture content transitionpattern at each of said discharge ends of said plurality of drying areasin a direction of travel of said web during times of changing said gradeof said web product from varying said steam pressure supplied to eachsteam-heated drum of said plurality of steam-heated drums at a giventime period and from repeatedly calculating, by said differenceequations, said moisture content transition pattern at a given timeperiod, while taking into consideration an assumptive time lag in aresponse of a temperature of each steam-heated drum of said plurality ofsteam-heated drums, and for simultaneously producing an associatedtemporal steam pressure transition pattern of each steam-heated drum ofsaid plurality of steam-heated drums during times of changing said gradeof said web product, in order to make said moisture content transitionpattern at each of said discharge ends of said plurality of drying areasduring predetermined times of changing said grade of said web productcoincide substantially with said desired moisture content pattern with apredetermined allowance; and means for adjustably changing said steampressure supplied to said respective stem-heated drums based upon saidsteam pressure transition pattern when actually changing said grade ofsaid web product on said paper machine.